IMFUFA-seminar: Geometric singular perturbation analysis
Lektor Kristian Uldall Kristiansen fra DTU Compute, Institut for Matematik og Computer Science taler om "Geometric singular perturbation analysis".
In dynamical systems theory, we have very powerful methods for the description of local phenomena. In contrast, the methods for global dynamics are in general much weaker, even for planar systems. This is the reason why Hilbert's 16th problem, on the number of limit cycles for planar polynomial vector fields, remains unsolved to this day (and probably will remain so, for many, many years to come!) However, if the system is singular, in some appropriate sense, then we can often solve global problems using singular perturbation theory.
In this talk, I will introduce geometric singular perturbation theory and demonstrate how it can be used to solve highly nontrivial, global problems in dynamics. I will present results from (low-dimensional) models on friction, piecewise smooth systems and biology. The blowup method is an essential technique for our approach to such problems. Ironically, we use this method to solve local problems by blowing them up to global ones!
Seminaret foregår på engelsk.
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